The Christensen measurable solutions of a generalization of the Gołąb-Schinzel functional equation. (English) Zbl 0860.39034

Brzdȩk, Janusz

Ann. Pol. Math. 64, No. 3, 195-205 (1996).

The main result in the paper is the following. Let \(X\) be a linear separable \(F\)-space over the set of real (or complex) numbers. If the real (or complex) valued function \(f\) satisfies \(f(x+f (x)^ny) = f(x)f(y)\) for all \(x,y \in X\) then \(f\) is either continuous or the set of points where \(f(x)\) is not zero is a Christensen zero set. All continuous solutions are determined.

Reviewer: J.Aczél (Waterloo/Ontario)

MSC:

39B52

Functional equations for functions with more general domains and/or ranges

Keywords:

Christensen measurable function; Golab-Schinzel equation; linear separable \(F\)-space; Christensen zero set; continuous solutions